From a pack of 52 cards, two cards are drawn together at random. What is the probability of both the cards being kings?

A. $$\frac{1}{15}$$

B. $$\frac{25}{57}$$

C. $$\frac{35}{256}$$

D. $$\frac{1}{221}$$

Answer: Option D

Solution(By Examveda Team)

Let S be the sample space
Then,
$$n(S) = $$ $${}^{52}\mathop C\nolimits_2 = $$ $$\frac{{\left( {52 \times 51} \right)}}{{\left( {2 \times 1} \right)}}$$   =1326
Let E = event of getting 2 kings out of 4
∴ $$n(E) = {}^4\mathop C\nolimits_2 = $$   $$\frac{{\left( {4 \times 3} \right)}}{{\left( {2 \times 1} \right)}}$$   = 6
∴ $$P(E) = \frac{{n(E)}}{{n(S)}} = $$   $$\frac{6}{{1326}} = \frac{1}{{221}}$$